Posted by **Jerry** on Saturday, July 18, 2009 at 11:56am.

Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24- hour cycle of sleeping and walking- even if they are not exposed to the usual pattern of sunlight. To test this notion, eight paid volunteers were placed (individually) in a room in which there was no light from the outside and no clocks or other indications of time. They could turn the lights on and off as they wished. After a month in the room, each individual tended to develop a steady cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25

Using the 5% level of significance, what should we conclude about the theory that 24 hours is the natural cycle? (That is, does the average cycle length under these conditions differ significantly from 24 hours?)

(a) Use the steps of hypothesis testing.

(b) Sketch the distributions involved.

(c) Explain your answer to someone who has never taken a course in statistics.

- statistics -
**MathGuru**, Saturday, July 18, 2009 at 8:14pm
You can probably use a one-sample t-test for this data. You'll need to calculate the mean and standard deviation. Here's a t-test formula:

t = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

Hypotheses:

Ho: µ = 24 -->null hypothesis

Ha: µ does not equal 24 -->alternate hypothesis

Once you do the calculations, use a t-table to determine the cutoff to reject the null at .05 level of significance for a two-tailed test using 7 degrees of freedom (df = n - 1 = 8 - 1 = 7).

Does the test statistic exceed the cutoff (critical) value from the table? If it does not, you cannot reject the null and conclude a difference. If it does, then reject the null and conclude a difference.

I hope this will help.

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